Electronic structures of intrinsic \textit{n}-type SrTiO$_{3}$-LaAlO$_{3}$ interface: density and spatial distribution of free carriers

The seminal paper by Ohtomo and Hwang reporting the unexpected conductivity when two perovskite insulators, SrTiO$_{3}$ and LaAlO$_{3}$, formed an atomically abrupt interface along [001] direction, has aroused an immense interest on the origin of the conductivity. While it is widely accepted that the intrinsic $n$-type interface is conducting, the carrier density and its spatial distribution are not fully understood. In presentation, first-principles study for establishing the fundamental property of the charge carrier in the intrinsic $n$-type LaAlO$_{3}$/SrTiO$_{3}$ interface is introduced. To this end, large model systems including up to 20 layers of SrTiO$_{3}$ and 1--10 layers of LaAlO$_{3}$ are employed. The charge carrier is observed when LaAlO$_{3}$ is larger than 3 unit cells and it converges to 0.5 electrons per unit cell. It is also found that the charge carriers transferred from LaAlO$_{3}$ surface are mostly localized within a few layers from the interface. Furthermore, the electronic states are quantized at the interface with different localization widths, which is similar to electrons in a wedge potential. The carrier density contributed by the interface-localized state shows a good agreement with the experiment.